One sample t testing
ONE Sample Statistical Testing
Statistical testing is crucial, nowadays, in all industries. Following the steps we can reach satisfied results about experiments with a small samples and economical methods. The package Rcmdr can be helpful in these tests.
We formulate the one sample t-testing problem first by giving hypothesis to our problem (Ho) is known as the null hypothesis and (H1) is known as the alternative hypothesis.
We must know the P-value, which can be defined as the probability to obtain the same value of the test if the value of Ho is true. If P-value is lower than of a pre-defined value (α), the null hypothesis is rejected and the alternative hypothesis is accepted.
If P-value ≥ α we accept Ho
If P-value < α we reject Ho
We will start by an example of one sample t-test from a real life case study; where we need to be sure if the filling yoghurt machine is working properly or not to fill one package by 100g. the data are given in the below table.
We will assume that Ho=µ=100g and H1=µ≠100g
| mass |
| 104.8 |
| 98.8 |
| 101.6 |
| 100.4 |
| 100.7 |
| 99.4 |
| 104.9 |
| 98.7 |
| 102.6 |
| 100.7 |
| 101.7 |
| 99.5 |
| 98.7 |
| 104.8 |
| 98.9 |
| 100 |
| 98.2 |
| 101.2 |
| 104.2 |
| 101.1 |
| 104.7 |
| 103.9 |
| 101.8 |
| 98.3 |
| 101.4 |
| 98.8 |
| 99.1 |
| 98.8 |
| 100.5 |
| 104.3 |
| 102.7 |
| 101.7 |
| 98 |
| 104.5 |
| 99.3 |
| 105 |
| 104.5 |
| 99.1 |
| 104.7 |
| 102.4 |
| 100.1 |
| 101 |
| 102.2 |
| 101.5 |
| 98.5 |
| 100.1 |
| 100.6 |
| 102 |
After uploading the data set, from Rcmdr press statistics then mean then one-sample t-test. In the below figure, the selected confidence level was 95% and the null hypothesis was 100 gm as shown in the below figure.
From the below figure, the results show that at the P-value is less than 0.05. Thus, we can conclude that at 95% confidence level there is a significant difference between the filled values and the required mean (100g).
From the previous article, we can not neglect the importance of R programming language in solving real life problems specially in quality control field for industrial applications
We need to thank you for following our blog and wait for us in the next interesting articles concerning statistics and industrial engineering field
Prepared by: Shady Magdy
